In joint work with Buryak, Pandharipande and Tessler (in
preparation), we define equivariant stationary descendent integrals
on the moduli of stable maps from surfaces with boundary to
$(\mathbb{CP}^1,\mathbb{RP}^1)$. For stable maps of the disk...
We will give a brief overview of the classical topics, problems and
results in Algebraic Combinatorics. Emerging from the
representation theory of $S_n$ and $GL_n$, they took a life on
their own via the theory of symmetric functions and Young...
A martingale is a sequence of random variables that maintain
their future expected value conditioned on the past. A
$[0,1]$-bounded martingale is said to polarize if it converges in
the limit to either $0$ or $1$ with probability $1$. A
martingale...
$p$-adic period spaces have been introduced by Rapoport and Zink as
a generalization of Drinfeld upper half spaces and Lubin-Tate
spaces. Those are open subsets of a rigid analytic $p$-adic flag
manifold. An approximation of this open subset is the...
Lattices are periodic arrangements of points in space that have
attracted the attention of mathematicians for over two centuries.
They have recently become an object of even greater interest due to
their remarkable applications in cryptography. In...
For initial datum of finite kinetic energy Leray has proven in 1934
that there exists at least one global in time finite energy weak
solution of the 3D Navier-Stokes equations. In this talk, I will
discuss very recent joint work with Vlad Vicol in...
Existing unconditional progress on the abc conjecture and Szpiro's
conjecture is rather limited and coming from essentially only two
approaches: The theory of linear forms in $p$-adic logarithms, and
bounds for the degree of modular parametrizations...
In the lectures I will formulate a conjecture asserting that
there is a hidden action of certain motivic cohomology groups on
the cohomology of arithmetic groups. One can construct this action,
tensored with $\mathbb C$, using differential forms...
Geometric Complexity Theory (GCT) was developed by Mulmuley and
Sohoni as an approach towards the algebraic version of the P vs NP
problem, VP vs VNP, and, more generally, proving lower bounds on
arithmetic circuits. Exploiting symmetries, it...
We will explain a definition of open Gromov-Witten invariants on
the rational elliptic surfaces and explain the connection of the
invariants with tropical geometry. For certain rational elliptic
surfaces coming from meromorphic Hitchin system, we...
